Intricate things are complex and have many elements: they're not simple. Think of the intricate wiring of a computer's motherboard, or the intricate plot of a movie that you have a hard time following.
Anything intricate is complicated. Chess is a very intricate game that you could study your entire life and still not know everything about. On the other hand, a game like Connect Four is not very intricate. The more details and parts something has, the more intricate it is. A two-part plan isn't very intricate. A 2000-step plan is intricate; it's harder to wrap your head around.